Problem: $\overline{AC}$ is $8$ units long $\overline{BC}$ is $4$ units long $\overline{AB}$ is $4\sqrt{5}$ units long What is $\sin(\angle ABC)$ ? $A$ $C$ $B$ $8$ $4$ $4\sqrt{5}$
Solution: SOH CAH TOA in = pposite over ypotenuse opposite $= \overline{AC} = 8$ hypotenuse $= \overline{AB} = 4\sqrt{5}$ $\sin(\angle ABC)=\frac{8}{4\sqrt{5}}$ $=\dfrac{2\sqrt{5} }{5}$